These days, a medical procedure known as “egg freezing,” also known as “oocyte cryopreservation,” is done to increase a woman’s window of fertility, which involves removing, freezing, and storing her eggs.These days, a medical procedure known as “egg freezing,” also known as “oocyte cryopreservation,” is done to increase a woman’s window of fertility, which involves removing, freezing, and storing her eggs.